Integration formulas

∫ dx

= x + C

∫ xʳ dx

= (xʳ⁺¹) / (r + 1) + C (r ≠ -1)

∫ cos x dx

sin x + C

∫ sin x dx

= -cos x + C

∫ sec² x dx

= tan x + C

∫ csc² x dx

= -cot x + C

∫ sec x tan x dx

= sec x + C

∫ csc x cot x dx

= -csc x + C

∫ eˣ dx

= eˣ + C

∫ bˣ dx

= (bˣ) / ln b + C (0 < b, b ≠ 1)

∫ (1 / x) dx

= ln |x| + C

∫ (1 / (1 + x²)) dx

= tan⁻¹ x + C

∫ (1 / √(1 - x²)) dx

= sin⁻¹ x + C

∫ (1 / (x√(x² - 1))) dx

= sec⁻¹ |x| + C

∫ c f(x) dx

= c ∫ f(x) dx

∫ [f(x) + g(x)] dx

= ∫ f(x) dx + ∫ g(x) dx

∫ [f(x) - g(x)] dx

= ∫ f(x) dx - ∫ g(x) dx

tan(x)=

Sine X over cosine X

csc(x)=

One over sine x

sec(x)=

One over cosine X

Cot x =

Cosine x over sine x

cos²(x) + sin²(x)=

1